[joshs]

You hold: 932 A5 T65 AKJ43

Auction your side slient:

LHO: 3N (Gambling solid minor, no outside A or K)
RHO: 5C( pass or correct)
LHO: 5S (Suprise, I guess 3N showed any solid suit....)
All Pass

Partner leads the heart Q (rusinow, showing the K or shortage)
Dummy comes down with: T 8742 AQJ32 T75

You play upside down count and attitude. Plan the defense.

Josh

[cherdano]

Hmm. Justin's plan fails when LHO has a heart single. Overtaking and playing club king fails when he has a club void. I think the void is less likely. In particular since with a void, 4♠ might be more attractive than 3N.

Arend

[joshs]

In general, a gambling 3N bid is not suppossed to contain a void, but it wasn't supposed to contain a major suit either, so who knows...

[Kalvan14]

Usually, advancer would have bid 4♦, which caters for all possible suits hold by the 3NTer.
I take the ♥A, and play the ♣K, to see a count in the suit.
A void should be less likely than a singleton (but then I've never seen anyone bidding 3NT with 8 solid spades)

[han]

Agree with Arend, overtaking followed by the club king seems best for his reason.

[Winstonm]

As there are two ways for 1-2/2-1 division and only one 3-0, I will play a small heart. Partner should now give me a count card with the club switch.

Winston

[joshs]

To everyone who overtook the heart and played the club K, partner will play the 2 showing 2 or 4, and you are guessing now.

I think overtaking at trick 1 is very wrong! But please feel free to elucidate me on your cashout carding methods...

Note: If you had been dealt the A2 doubleton, both players would know the heart count at trick 2 if you follow with the 2 since partner will continue with 3 or 5 and switch with 4 or 6. So if he switches to a club, he will lead 3/low and you hopefully will be able to read that card. With the A5 (the second lowest outstanding spot) partner will probably be able to read the count, but its not foolproof.

But I am interested to hear about other carding methods for these situations.

Josh

[Winstonm]

If partner has 6 hearts and the Q holds the trick, he will know the heart count anyway regardless of whether I have the 5 or 2. My plan is to play opener for either 1/2 or 2/1 instead of 3-0 in the side suits. Playing UDCA, partner should know the 5 would not be the play from A52 so if he has 5 hearts he can continue - with 6 he should switch to a count card in clubs.

Winston

[joshs]

Kalvan14, on Jan 30 2006, 09:42 PM, said:

Usually, advancer would have bid 4♦, which caters for all possible suits hold by the 3NTer.
I take the ♥A, and play the ♣K, to see a count in the suit.
A void should be less likely than a singleton (but then I've never seen anyone bidding 3NT with 8 solid spades)

Actually, the usual method over gambling 3N (which is suppossed to only be a minor) is to play:
4C pass or correct
4D do you have a singleton: 4H heart singleton, 4S spade singleton, 4N no, 5C (diamond singleton), 5D (club singleton)
4M natural
4N do you have an 8'th card?
5C pass or correct

[joshs]

Winstonm, on Jan 31 2006, 11:48 AM, said:

If partner has 6 hearts and the Q holds the trick, he will know the heart count anyway regardless of whether I have the 5 or 2. My plan is to play opener for either 1/2 or 2/1 instead of 3-0 in the side suits. Playing UDCA, partner should know the 5 would not be the play from A52 so if he has 5 hearts he can continue - with 6 he should switch to a count card in clubs.

Winston

Yes if he has 6 he will always switch no matter what my count card was, but if he switches you don't know he has 6. He would also switch with 4 if he can read your count card.

Its just a bit interesting how the defensive inferences vary with the size of your second heart.

Josh

[joshs]

Jlall, on Jan 31 2006, 11:59 AM, said:

joshs, on Jan 31 2006, 11:56 AM, said:

Yes if he has 6 he will always switch no matter what my count card was, but if he switches you don't know he has 6. He would also switch with 4 if he can read your count card.

Its just a bit interesting how the defensive inferences vary with the size of your second heart.

Josh

If you overtake and play a heart he will know you have a doubleton and will always do the right thing if there is something to be done.

Well if thats your defense, declarer makes 6... (Partner has 6 hearts)

I think the point of the problem here, is to come up with a plan that gives you the highest probability of cashing 3 tricks. Good carding methods might also help.

[joshs]

Jlall, on Jan 31 2006, 12:46 PM, said:

joshs, on Jan 31 2006, 12:29 PM, said:

Well if thats your defense, declarer makes 6... (Partner has 6 hearts)

I know, I knew the hand before I posted on this thread. I don't see the relevance.

Ahh, well then maybe I didn't understand your point. I think there is an algorithm here that cashes out successfully 80% of the time when what you do matters (e.g. partner has 6 hearts OR 4 clubs), and not the 62.5% odds you get when you overtake.

Let me first suppose you had the A2 of hearts and not the A5. This is unambigously readable as 2 or 4.
If partner has 3 or 5 hearts he continues and there is no problem (assuming no club void).
So if partner switches to a club he has 4 or 6 hearts.

If you can read the spot card as definitely 2 or 3 clubs, you have no problem.
If you can't tell if he is 3 or 4, you have a guess what to play back.

Lets see how this algorithm does on the critical lengths:

Lets let p andq denote the probability that the club spot is readable as being from 3 or 4. (assuming 3 and low shifts) when partner has 3 or 4 respectively. First lets assume that p=q (I don't think they are equal)

When partner has a doubleton and shifts there is only ambiguity when he has the two lowest outstanding spots (1 of ten possibilities) (e.g. 90% of the time the shift is readable as NOT from 4, the other 10% of the time you have to guess)


a. 6H 2C : 95%
b. 6H 3C : = 1-(1-p)/2
c. 5H 4C : 100%
d. 4H 4C : = 1-(1-p)/2

If these 4 cases are equally likely then the algorithm works
: 97.5-(1-p)/4 % of the time.

if P=0 then its 72.5%, and p is higher than 0 (lowest club card is always readable as being from 3). I suspect that p will be more than 20% (more if declarer occasionally forgets to false card), which gives you 77.5%.

With the A5 (second lowest available spot) partner will not know the heart count 100% of the time, so this will diminish your probability of success, but not by that much.


The overtake, cash a club, and then guess if the answer is even algorithm works:
250/4=62.5% of the critical cases

The over take and return one algorithm works 50% of the time.


Since I am at it lets work out p and q. partner leads the 3'rds 4'th or 5'th lowest spot.
If its the 5'th, its always readable.
if its the 4'th, and declarer always plays a higher card if he has one. Its never readable
if its the 3'rd then its never readable.

so 3 card holdings, ranked with 1 highest and 5 lowest card:
123
124
125
134
135
145
234
235
245
345
=readable 6/10 times

4 card holdings:
1234
1235
1245
1345
2345
=readable 0/5 times

hence p=.6 and q=0

so the actual calculation gives:

a. 6H 2C : 95%
b. 6H 3C : = 1-(1-p)/2=80%
c. 5H 4C : 100%
d. 4H 4C : = 1-(1-q)/2=50%

So the algorithm (low at trick 1, etc.) gives: 325/4=81.25% probability of success for the critical cases if you held the A2.



Being tierd at this point, I will attempt to work out the odds with A5 later...

Josh

[joshs]

Calculation continued:

With A5:
If partner has 6 hearts he knows the position
If partner has 5 hearts, he has 3 smaller unseen cards than the Q and declarer has 1, so he knows the position 75% of the time (assuming the manditory falsecard)
If partner has 4 hearts, he has 2 smaller cards and so does decalrer, so he knows the position 50% of the time, and should always switch, just as he would if he actually new the position
If decalrer has 3 hearts, he should always continue assuming you lead the K from KQ doubleton (since with Axxxxx you would overtake and switch and not give count), so there is still no critical case with him having 3 hearts (and besdies the opening bid was really looney then).


Now first algorithm: you assume partner knows the heart count

a: 95% like before
b. 80% like before
c. he continues 75% of the time and swtiches 25% of the time. After he switches you have a 50% chance of guessing what to do. = 87.5%
d. 50% like before

Total=312.5/4=78.125%

Maybe there is something better than a coin flip at the end if the club switch was unreadable?

Josh

[Kalvan14]

joshs, on Jan 31 2006, 11:29 AM, said:

To everyone who overtook the heart and played the club K, partner will play the 2 showing 2 or 4, and you are guessing now.

I think overtaking at trick 1 is very wrong! But please feel free to elucidate me on your cashout carding methods...

Note: If you had been dealt the A2 doubleton, both players would know the heart count at trick 2 if you follow with the 2 since partner will continue with 3 or 5 and switch with 4 or 6. So if he switches to a club, he will lead 3/low and you hopefully will be able to read that card. With the A5 (the second lowest outstanding spot) partner will probably be able to read the count, but its not foolproof.

But I am interested to hear about other carding methods for these situations.

Josh

If partner signals 2 or 4 clubs after A♥ and K♣, it becomes a guess. 6-1 in hearts should be less likely than 4-1 in clubs, for what is worth in this hand, where declarer holds an 8-card suit. If (as I gather from your post) you play reverse count, and with a doubleton or 4 cards partner leads the smallest, there is no way to read his actual holding.


As far as the structure of answers after a Gambling 3NT, I'll never go for a complicated convention for a hand which has a very low frequency.
As a matter of fact, I do not even play Gambling 3NT in my established partnerships.

[joshs]

Kalvan14, on Jan 31 2006, 06:33 PM, said:

joshs, on Jan 31 2006, 11:29 AM, said:

To everyone who overtook the heart and played the club K, partner will play the 2 showing 2 or 4, and you are guessing now.

I think overtaking at trick 1 is very wrong! But please feel free to elucidate me on your cashout carding methods...

Note: If you had been dealt the A2 doubleton, both players would know the heart count at trick 2 if you follow with the 2 since partner will continue with 3 or 5 and switch with 4 or 6. So if he switches to a club, he will lead 3/low and you hopefully will be able to read that card. With the A5 (the second lowest outstanding spot) partner will probably be able to read the count, but its not foolproof.

But I am interested to hear about other carding methods for these situations.

Josh

If partner signals 2 or 4 clubs after my overtaking with the A♥ and playing the K♣, there is no guess: play ♥.

Declarer can have 2 possible hands which matter:

AKQxxxxx xx xx x (partner has 4 clubs)
or
AKQxxxxx x x xxx (partner has 2 clubs).

The first case is the dangerous one (8 spades + 3 diamonds on a successful finesse).

In the second case, declarer is limited to 10 tricks.


As far as the structure of answers after a Gambling 3NT, I'll never go for a complicated convention for a hand which has a very low frequency.
As a matter of fact, I do not even play Gambling 3NT in my established partnerships.

Huh?

1. Gambling 3N is usually only a 7 card suit, it can be 8, but its not usually
2. Declarer's hand WAS: AKQxxxx x xx xxx so your "there is no guess algorithm" just let declarer make.

3. If declarer's hand was AKQxxxxx x x xxx (your 2'nd hand) then after declarer ruffs and plays all but one trump the position is:


Declarer: 1 trump, 1 diamond, 2 clubs
Dummy: AQJ of diamonds and a heart
Partner Kxx of diamonds and a good heart

You some good clubs, but you have no hearts left

So when declarer plays his last trumps partner is squeezed. in diamonds and hearts. If partner throws a diamond, declarer throws a heart, takes a diamond hook, and his other diamonds are good. If partner throws the heart, declarer throws a diamond, takes a diamond hook, and dummy is good.


Josh